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Application of new and accurate methods of estimating breeding values and systematic selection based on performance characters have increased the complexity of animal breeding. Negative correlations between the most important characters may be involved, especially in the selection of dairy and beef cattle. This problem demands efficient selection models to maximize genetic improvement of some economic traits and simultaneously to restrict other antagonistic traits to a certain genetic change. We have established a general theory of selection indexes with constraints to impose fixed and proportional restrictions when several selection indexes containing different information sources are applied. A detailed description of the iterative computing procedure used to determine the restricted index weights is presented in this report. For demonstrating the procedure, the effects of fixed and proportional restrictions imposed on genetic change in milk, growth, reproduction and carcass traits of cattle were investigated. Findings show that genetic progress in some economic traits is still possible when genetic change of other economic, but antagonistic traits, is positive or set equal to zero.